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Friday, December 08, 2006

I remember reading, years ago, the excellent book "The Psychology of Mathematical Invention" by the mathematician Jacques Hadamard...

He surveyed a bunch of mathematicians, intending to find out how mathematicians think internally. Many mathematicians thought visually, it was found; some thought in terms of sounds, some purely abstractly.

But, George Polya was the only mathematician surveyed who claimed to think internally in terms of grunts and groans like "aaah", "urrghhh" , "hmtphghhghggg"....

At the time I read this, I thought it was very odd.

However, now I have just read Mithen's book ("The Singing Neanderthals", discussed in another, recent blog of mine) claiming that the language of Neanderthals and early Cro-magnons was like that: no words, just lengthy, semi-musical grunts and groans with varying intonation patterns....

So maybe Polya was just old-fashioned.... ;-)

Anyone else out there think in terms of grunts and groans and so forth? If so please contact me....

Saturday, December 02, 2006

My son Zebulon (age 13) recently had to write a brief essay for school on "My Favorite Place," as part of a national essay competition. His essay was chosen to represent his school in the county-wide competition. His theme was an amusing one which may resonate with many readers of this blog -- the third paragraph particularly reminds me of myself on some of my more productive days! (But Zeb is not working on AI, he's working on animations, see zebradillo.com)

My Favorite PlaceZebulon Goertzel

I work my way past all the furniture in my cramped room and sit down at my chair. I see a computer, a laptop. On its screen are pixels. Tiny, stabbing rays of color that drill into my eyes and let me enjoy my computer to no end despite its hideous flaws. The monitor is marked and scarred due to various past and unknown misuses. The dull keyboard is with its regular layout, usable but without an S key. I look at the front disk drive and recall being told not to remove it.

Beside my laptop is my tablet. In its middle-left side is the pen, a gnawed-on, well-used device that is often lost and found in my pocket. The tablet cover is not without scratches, some deep, some light. Each scratch is from a scribble or drawing or line somebody drew. A bright wire links my tablet to the sloppy tangle of wires, connectors and cables which is usually behind my laptop.

My computer’s fan consistently buzz-whirs with high pitch. I am hypnotized as I slowly lean forward, as I grip my tablet pen with sore, almost numb fingers, as I click and click and click. My back is hunched and my neck is out. I work. My eyes ache, but I hardly notice. My stomach is empty, but I try to ignore it. I decide to be done. I get up, stretch, and go to care for myself. My favorite place is my computer, or my desk, because there are no limits to what a computer can do, and my computer fascinates me to no end.

In one of those pleasant synchronicities, a couple days ago PJ Manney started a conversation with me about music and the scientific mind, at the same time as I received in the mail a book I had ordered a couple weeks ago, "The Singing Neanderthals," about the cognitive origins of music.

So, here I'll start with some personal notes and musings in the musicaloidal direction, and finally wander around to tying them in with cognitive theory...

I had told PJ I was a spare-time semi-amateur musician (improvising and composing on the electronic keyboard -- yeah, one of these days I'll put some recordings online; I keep meaning to but other priorities intervene) and she was curious about whether this had had any effect on my AI and other scientific work.

I mentioned to her that I often remember how Nietzsche considered his music improvisation necessary to his work as a philosopher. He kept promising himself to stop spending so much time on it, and once said something like "From now on, I will pursue music only insofar as it is domestically necessary to me as a philosopher."

This is a sentiment I have expressed to myself many times (my music keyboard being a tempting 10 feet away from my work desk...). Like Nietzsche, I have found a certain degree of musicological obsession "domestically necessary" to myself as a creative thinker.... The reasons for this are interesting to explore, although one can't draw definite conclusions based on available evidence....

When I get "stuck" thinking about something really hard, I often improvise on the piano. That way one of two things happens: either

1) my mind "loosens up" and I solve the problem

or

2) I fail to solve the problem, but then instead of being frustrated about it, I abandon the attempt for a while and enjoy myself playing music ;-)

Improvising allows one's music to follow one's patterns of thought, so the music one plays can sorta reflect the structure of the intellectual problem one is struggling with....

I drew on my experiences composing/improvising music when theorizing about creativity and its role in intelligence, and cooking up the aspects of the Novamente AGI design that pertain to flexible creativity....

As well as composing and improvising, I also listen to music a lot -- basically every kind of music except pop-crap and country -- most prototypically, various species of rock while in the car, and instrumental jazz/jazz-fusion when at home working ... [I like music with lyrics, but I can't listen to it while working, it's too distracting... brings me back too much to the **human** world, away from the world of data structures and algorithms and numbers!! ... the nice thing with instrumental music is how it captures abstract patterns of flow and change and interaction, so that even if the composer was thinking about his girlfriend's titties when he wrote the song, the abstract structures (including abstract **emotional** structures) in the music may feel (and genuinely **be**) applicable to something in the abstract theory of cognition ;-) ] ... but more important than that is the almost continual unconsciously-improvised "soundtrack" inside my head. It's as though I'm thinking to music about 40% of the time, but the music is generated by my brain as some kind of interpretation of the thoughts going on.... But yet when I try to take this internal music and turn it into **real music** at the keyboard, the translation process is of course difficult, and I find that much of the internal music must exist in some kind of "abstract sound space" and could never be fully realized by any actual sounds.... (These perverted human brains we are stuck with!!!)

Now, on to Mithen's book "The Singing Neanderthals," which makes a fascinating argument for the centrality of music in the evolution of human cognition.... (His book "The Prehistory of Mind" is really good as well, and probably more of an important work overall, though not as pertinent to this discussion...)

In brief he understands music as an instantiation and complexification of an archaic system of communication that was based (not on words but) on patterns of vocal tonal variation.

(This is not hard to hear in Radiohead, but in Bach it's a bit more sublimated ;=)

This ties in with the hypothesis of Sue Savage-Rumbaugh (who works with the genius bonobo Kanzi) that language likely emerged originally from protolanguages composed of **systems of tonal variation**.

Linguist Alison Wray has made related hypotheses: that protolanguage utterances were holistic, and got partitioned into words only later on. What Savage-Rumbaugh adds is that before protolanguage was partitioned into words, it was probably possessed of a deep, complex semantics of tonal variation. She argues this is why we don't recognize most of the existing language of animals: it's not discrete-word language but continuous-tonal-variation language.

(Funny that both these famous theorists of language-as-tonal-variation are women! I have sometimes been frustrated by my mom or wife judging my statements not by their contents but by the "tone" of delivery ;-)

This suggests that a nonhuman AI without a very humanlike body is never going to experience language anywhere near the same way as a human. Even written language is full of games of implied tonal variation-pattern; and in linguistics terms, this is probably key to how we select among the many possible parses of a complex sentence.

[Side note to computational linguists and pragmatic AI people: I agree the parse selection problem can potentially be solved via statistics, like Dekang Lin does in MiniPar; or via pure semantic understanding, as we do when reading Kant in translation, or anything else highly intellectual and non-tonal in nature.... But it is interesting to note that humans probably solve parse selection in significant part thru tonal pattern recognition....]

Regarding AI and language acquisition, this line of thinking is just a further justification of taking a somewhat nonhumanlike approach to protolanguage learning; as if this sort of theory is right, the humanlike approach is currently waaay inaccessible to AI's, even ones embodied in real or simulated robots... It will be quite a while until robot bodies support deep cognitive/emotional/social experience of tonal variation patterns in the manner that we humans are capable of.... The approach to early language learning I propose for Novamente is a subtle combination of humanlike and nonhumanlike aspects.

More speculatively, there may be a cognitive flow-through from "tonal pattern recognition" to the way we partition up the overall stream of perceived/enacted data into events -- the latter is a hard cognitive/perceptual problem, which is guided by language, and may also on a lower level be guided by subtle tonal/musical communicative/introspective intuitions. (Again, from an AI perspective, this is justification in favor of a nonhumanlike route ... one of the subtler aspects of high-level AI design, I have found, is knowing how to combine human-neurocognition inspiration with computer-science inspiration... but that is a topic for another blog post some other day...)

I am also reminded of the phenomenon of the mantra -- which is a pattern of tonal variation that is found to have some particular psychospiritual effect on humans. I have never liked mantras much personally, being more driven to the spare purity of Zen meditation (in those rare moments these days when emptying the intellectual/emotional mind and seeking altered states of purer awareness seems the thing to do...); but in the context of these other ideas on music, tones and psychology, I can see that if we have built-in brain-wiring for responding to tonal variation patterns, mantras may lock into that wiring in an interesting way.

I won't try to describe for you the surreal flourish of brass-instrument sounds that I hear in my mind at this moment -- a celebratory "harmony of dissonance" tune/anti-tune apropos of the completion of this blog post, and the resumption of the software-code-debugging I was involved with before I decided to distract myself briefly via blogging...

Friday, November 10, 2006

Last night, at the offices of the Electric Sheep Company (a company devoted to creating "virtual Real Estate" in multi-participant online simulation worlds such as Second LIfe), I saw Sibley Verbeck give a lovely presentation on the state of the art in these proto-Metaverse technologies.

These days, more than 10K people are online in Second Life at any given moment, it seems. A million subscribers, half of them active. People are talking about the potential for using Second Life for business presentations, as a kind of super-pumped-up 3D avatar-infused WebEx. And of course the possibility for other cool apps not yet dreamed of.

Stirring stuff ... definitely, technology worth paying attention to.

And yet, Sibley's excellent presentation left me wondering the following: Do we really want to perpetuate all the most stupid and irritating features of human society in the metaverse ... such as obsession with fashion and hairstyles!!??

"Virtual MTV Laguna Beach", a non-Second-Life project that Electric Sheep Factory did, is technically impressive yet morally and aesthetically YUCK, from a Ben Goertzel perspective. Virtual So-Cal high school as a post-Singularity metaverse is a kind of transhumanist nightmare.

I remain unclear regarding whether there will really be any **interesting** "killer apps" for metaverse technology (and I don't find gaming or online dating all that interesting ;) before really powerful multisensory VR interfaces come about.

And even then, simulating humanity in virtuo fascinates me far less than going beyond the human body and its restrictions altogether.

But, I do note that we are currently using a 3D sim world to teach our Novamente baby AI system. Once it becomes smarter, perhaps we will release our AI in Second Life and let it learn from the humans there ... about important stuff like how to wear its hair right (grin!)

And I must admit to being excited about the potential of this sort of tech for scientific visualization. Flying your avatar through the folds of a virtual human brain, or a virtual cell full of virtual DNA, would be mighty educational. Not **fundamental** in the sense of strong AI or molecular assemblers or fully immersive VR, but a lot niftier than Virtual Laguna Beach....

Thursday, November 02, 2006

This is just a quick follow-up to the prior post on "Being a Force of Nature" ...

Thinking over the issues I wrote about in that post, I was reminded of a failed attempt I made many years ago to construct a more robust kind of music theory than the ones that currently exist....

(Ray Jackendoff's generative-grammar-based theory of music is a nice attempt in a similar direction to what I was trying to do, but ultimately I think he failed also....)

Existing music theory seems not to address the most important and interesting questions about music: Which melodies and rhythms are the most evocative to humans, in which ways, and why?

To put it crudely, we know how to distinguish (with fairly high accuracy) a horrible melody from an OK-or-better melody based on automated means. And we know how to distinguish (with fairly high accuracy) what sorts of emotions an OK-or-better melody is reasonably likely to evoke, by automated means.

But, we have NO handle whatsoever, scientifically or analytically, on what distinguishes a GREAT melody (or rhythm, though I've thought most about melodies) from a mediocre one.

I spent a fair bit of time looking for patterns of this nature, mostly eyeballing various representations of melodies but also using some automated software scripts. No luck ... and I long ago got to busy to keep thinking about the issue....

What was wrong with this pursuit was, roughly speaking, the same thing that's wrong with thinking about human minds as individual, separate, non-social/cultural entities....

A musical melody is a sequence of notes arranged in time, sure ... but basically it's better thought of as a kind of SOFTWARE PROGRAM intended to be executed within the human acoustic/cognitive/emotional brain.

So, analyzing melodies in terms of their note-sequences and time-delays is sort of like analyzing complex software programs in terms of their patterns of bits. (No, it's not an exact analogy by any means, but you may get the point.... The main weaknesses of the analogy are: notes and delays are higher-level than bits; and, musical melodies are control-sequences for a complex adaptive system, rather than a simpler, more deterministic system like a von Neumann computer.)

In principle one could find note/delay-level patterns to explain what distinguishes good from great music, but one would need a HUGE corpus of examples, and then the patterns would seem verrrry complex and tricky on that level.

A correct, useful music theory would need to combine the language of notes and delays and such with the language of emotional and cognitive responses. The kind of question involved is: in a given emotional/cognitive context, which specific note/delay patterns/combinations provide which kinds of shifts to the emotional/cognitive context.

However, we currently lack a good language for describing emotional/cognitive contexts.... Which makes the development of this kind of music theory pretty difficult.

So in what sense is music a force of nature? A piece of music comes out of the cultural/psychological/emotional transpersonal matrix, and has meaning and pattern mainly in combination with this matrix, as a sequence of control instructions for the human brains that form components of this matrix...

(I am reminded of Philip K. Dick's novel VALIS, in which a composer creates music that is specifically designed to act on human brains in a certain way, designed to bring them to certain spiritual realizations. Before ever reading Dick, in my late teens, I had a fantasy of composing a musical melody that was so wonderfully recursively revelatory -- in some kind of Escher-meets-Jimi-Hendrix-and-Bach sort of way -- that it would wake up the listener's mind to understand the true nature of the universe. Alas, I've been fiddling at the piano keyboard for years, and haven't come up with it yet....)

Anyway, this is far from the most important thing I could be thinking about! Compared to artificial general intelligence, music is not so deep and fascinating ... ultimately it's mostly a way of fiddling with the particularities of our human mental system, which is not so gripping as the possibility of going beyond these particularities in the right sort of way....

But yet, in spite of its relative cosmic unimportance, I can't really stay away from music for too long! The KORG keyboard sitting behind me tempts ... and many of my best ideas have come to me in the absence/presence that fills my mind while I'm improvising in those quasi-Middle-Eastern scales that I find so seductive (and my daughter, Scheherazade, says she's so sick of hearing, in spite of her Middle-Eastern name ;-)

led me inevitably to thoughts about the useful (but sometimes counterproductive) illusions of self and free will.

The authors argue that one path to achieving great things and great happiness is to let go of the illusion of autonomy and individual will, and in the words of George Bernard Shaw "be a force of nature," allowing oneself to serve as a tool of the universe, of larger forces that exist all around and within oneself, and ultimately are a critical part of one's own self-definition (whether one always realizes this or not).

The Shaw quote says:

"This is the true joy in life, the being used for a purpose you consider a mighty one, the being a force of nature, rather than a feverish, selfish clod of ailments and grievances complaining that the world will not devote itself to making you happy."

A related quote from Martin Buber says of the "truly free" man, that he:

"... intervenes no more, but at the same time, he does not let things merely happen. He listens to what is emerging from himself, to the course of being in the world; not in order to be supported by it, but in order to bring it to reality as it desires."

There is an interesting dilemma at the heart of this kind of wisdom, which is what I want to write about today.

A part of me rebels strongly against all this rhetoric about avoiding individual will and being a force of nature. After all, nature sucks in many ways -- nature "wants" me and my wife and kids and all the rest of you humans to die. What the natural and cultural world around me desires is in large measure repellent to me. I don't want to "get a haircut and get a real job" just because that's what the near-consensus of the world around me is ... and nor do I want to submit to death and disease. Nor do I want to listen to everything that nature has put inside me: anger, irrationality and the whole lot of it.... Nature has given me some great gifts and some nasty stuff as well.

Many of the things that are important to me are -- at least at first glance -- all about me exercising my individual will against what nature and society want me to do. Working to end the plague of involuntary death. Working to create superhuman minds. Composing music in scales few enjoy listening to; writing stories with narrative structures so peculiar only the really open-minded can appreciate them. Not devoting my life entirely or even primarily to the pursuits of money, TV-viewing, and propagating my genome.

On the other hand, it's worth reflecting on the extent to which the isolation and independence of the individual self is an illusion. We humans are not nearly so independent as modern Western -- and especially American -- culture (explicitly and implicitly) tells us. In fact the whole notion of a mind localized in a single body is not quite correct. As my dear friend Meg Heath incessantly points out, each human mind is an emergent system that involves an individual body, yes, but also a collection of tools beyond the body, and a collection of patterns of interaction and understanding within a whole bunch of minds. In practice, I am not just who I am inside my brain, I am also what I am inside the brains of those who habitually interact with me. I am not just what I do with my hands but also what I do with my computer. I wouldn't be me without my kids, nor without the corpus of mathematical and scientific knowledge and philosophical ideation that I have spent a large bulk of my life absorbing and contributing to.

So, bold and independent individual willfulness is, to an extent, an illusion. Even when we feel that we're acting independently, from the isolation of our own heart and mind, we are actually enacting distributed cultural and natural processes. A nice illustration of this is the frequency with which scientific discoveries -- even revolutionary ones -- are made simultaneously by multiple individuals. Charles Darwin and Alfred Russell Wallace were being willful, independent, deviant thinkers -- yet each of them was also serving as a nodal point for a constellation of forces existing outside himself ... a constellation of forces that was almost inevitably moving toward a certain conclusion, which had to be manifested through someone and happened to be manifested through those two men.

An analogy appears to exist with the representation of knowledge in the human brain. There is a peculiar harmony of localization and distribution in the way the brain represents knowledge. There are, in many cases, individual and highly localized brain regions corresponding to particular bits of knowledge. If you remove that little piece of the brain, the knowledge may go away (though in many but not all cases, it may later be regenerated somewhere else). But yet, that doesn't mean the knowledge is immanent only in that small region. Rather, when the knowledge is accessed or utilized or modified, a wide variety of brain regions may be activated. The localized region serves as a sort of "trigger" mechanism for unlocking a large-scale activation pattern across many parts of the brain. So, the knowledge is both localized and distributed: there are globally distributed patterns that are built so as to often be activated by specific local triggers.

We can look at humans as analogous to neurons, in the above picture. None of us contains that much in and of ourselves, but any one of us may be more or less critical in triggering large-scale activation patterns ... which in turn affect a variety of other individuals in a variety of ways....

So then, the trick in being a "force of nature" is to view yourself NOT as an individual entity with an individual mind contained in an individual body, making individual decisions ... but rather, as a potential trigger for global activity patterns; or, to put it slightly differently, as a node or nexus of a whole bunch of complex global activity patterns, with the capability to influence as well as be influenced.

When we act -- when we feel like "we" are "acting" -- it is just as fair to say that the larger (social, cultural, natural, etc.) matrix of patterns that defines us is acting thru the medium of us.

I feel analytically that what I said in the previous paragraph is true... but what is interesting is how rarely I actually feel that way, in practice, in the course of going about my daily business. Even in cases where it is very obviously the truth -- such as my work on artificial general intelligence. Yes, I have willfully chosen to do this, instead of something else easier or more profitable or more agreeable to others. On the other hand, clearly I am just serving as the tool of a larger constellation of forces -- the movement of science and technology toward AGI has been going on a long time, which is why I have at my disposal the tools to work on AGI; and a general cultural/scientific trend toward legitimization of AGI is beginning, which is why I have been able to recruit others to work on AGI with me, which has been an important ingredient for maintaining my own passion for AGI at such a high level.

How different would it be, I wonder, if in my individual daily (hourly, minutely, secondly) psychology, I much more frequently viewed myself as a node and a trigger rather than an individual. A highly specialized and directed node and trigger, of course -- not one that averages the inputs around me, but one that is highly selective and responds in a very particular way intended to cause particular classes of effects which (among other things) will come back and affect me in specific ways.

In short: Letting go of the illusion of individuality, while retaining the delights of nonconformity.

Easy enough to say and think about; and rather tricky to put into practice on a real-time basis.

Cultures seem to push you either to over-individualism or over-conformity, and finding the middle path as usual is difficult -- and as often, is not really a middle path, in the end, but some sort of "dialectical synthesis" leading beyond the opposition altogether and into a different way of being and becoming....

Sunday, September 10, 2006

Wow, it's been a long time since I've blogged on here -- apparently I haven't been in a bloggy mood.

It's been a busy year ... I've sent my oldest son Zarathustra off to college at age 16 (to Simon's Rock College, www.simons-rock.edu, the same place I, my sister and my ex-wife went way back in the day), which is a very odd feeling ... I finished a pretty decent draft of a novel, Echoes of the Great Farewell, which is a completely lunatic prose-poetic novel-thing told from the stream-of-consciousness point of view of a madman who believes that hallucinogenic mushrooms have told him how to create a superhuman AI (perhaps I'll actually try to get this one published, though it's not a terribly publisher-friendly beast) ... I came up with a substantial simplification of the Novamente AI design, which I'm pretty happy with due to its deep foundations in systems philosophy ... worked with my Novamente colleagues to take a few more incremental steps toward implementation of the Novamente AGI design (especial progress in the area of probabilistic reasoning, thanks to the excellent efforts of Ari Heljakka) ... did some really nice data mining work in the context of some commercial projects ... make some freaky instrumental music recordings that my wife at least enjoyed ... hiked the Na Pali Trail on Kaui and a whole bunch of trails near the Matterhorn in the Alps with my mountain-maniacal young wife Izabela ... co-organized a conference (the AGIRI workshop) ... published a philosophy book, The Hidden Pattern, which tied together a whole bunch of recent essays into a pretty coherent statement of the "world as pattern" perspective that has motivated much of my thinking ... developed a new approach to AGI developmental psychology (together with Stephan Vladimir Bugaj) ... starred in a few animations created by my son Zebulon (zebradillo.com), including one about rogue AI and another in which I mercilessly murder a lot of dogs ... helped discover what seems to be the first plausible genetic underpinnings for Chronic Fatigue Syndrome (together with colleagues at the CDC and Biomind LLC) ... and jeez, well this list is dragging on, but it's really not the half of it...

A pretty full year -- fun to live; too much going on to permit much blogging ... but frustrating in the big picture, given that it's been yet another year in which only modest incremental progress has been made toward my most important goal of creating AGI. My understanding of AGI and the universe has increased significantly this year so far, which is important. And the Novamente codebase has advanced too. Again, though, balancing the goal of achieving AGI with the goal of earning cash to support a family (send the kids to college, pay the alimony (which runs out in another 9 months -- yay!!), etc.) proves a tough nut to crack, and is just a dilemma I keep living with, without solving it satisfactorily so far.... I'll be spending much of the next 6 weeks trying to solve it again, by doing a bunch of meetings and social-networking events partially aimed at eventually putting me in touch with investors or other partners who may be interested in funding my AGI work more fully than is currently the case. (Don't get me wrong, we are moving toward AGI in the Novamente project right now, but we could be moving 10 times faster with some fairly modest investment ... the small amount of investment we've gotten so far, combined with the small surplus value my colleauges and I have managed to extract from our commercial narrow-AI contracts, is far from enough to move us along at maximum rate.)

BUT ANYWAY ... all this was not the point of this blog entry. Actually, the point was to give a link to an essay I wrote on a train from Genova to Zermatt, following a very interesting chat with Shane Legg and Izabela. Shane wrote a blog entry after our conversation, which can be found by going to his site

The essay is informal in the sense of a blog entry, but is too long to be a blog entry. My argument is a bit more positive than Shane's in that, although I agree with him that guaranteeing "AI Friendliness" in a Yudkowskian sense is very unlikely, I think there may be more general and abstract properties ("compassion" (properly defined, and I'm not sure how), anyone?) that can be more successfully built into a self-modifying AI.... (Shane by the way is a deep AI thinker who is now a PhD student working with Marcus Hutter on the theory of infinitely powerful AI's, and who prior to that did a bunch of things including working with me on the Webmind AI system in the late 1990's, and working with Peter Voss on the A2I2 AGI architecture.)While you're paying attention, you may be interested in another idea I've been working on lately, which is a variant of the Lojban language (tentatively called Lojban++) that I think may be very useful for communication between humans and early-stage AGI's. If you're curious you can read about it at

With a view toward making Lojban++ into something really usable, I've been spending a bit of time studying Lojban lately, which is a slow but fascinating and rewarding process that I encourage others to undertake as well (see www.lojban.org).

Well, OK ... that's enough for now ... time for bed. (I often like late-night as a time for work due to the quiet and lack of interruptions' but tonight my daughter is having a friend sleep over and they're having an extremely raucous post-midnight mop-the-dirty-kitchen-floor/mock-ice-skating party which is more conducive to blogging than serious work ;-). I hope to blog a bit more often in the next months; for whatever obscure human-psychology reason it seems to gratify some aspects of my psyche. Hopefully the rest of 2006 will be just as fun and diverse as the part so far -- and even more productive for Novamente AGI...

Wednesday, January 25, 2006

This blog entry arises from an email I sent to the SL4 email list, in response to a suggestion by Marc Geddes that perhaps the universe can best be considered as a logically inconsistent formal system.

I find that Marc's suggestion ties in interestingly with a prior subject I've dealt with in this blog: Subjective Reality.

I think it is probably not the best approach to think about the universe as a formal system. I find it more useful to consider formal systems as approximate and partial models of the universe.

So, in my view, the universe is neither consistent nor inconsistent, any more than a brick is either consistent or inconsistent. There may be mutually consistent or mutually inconsistent models of the universe, or of a brick.

The question Marc has raised, in this perspective, is whether the "best" (in some useful sense) way of understanding the universe involves constructing multiple mutually logically inconsistent models of the universe.

An alternative philosophical perspective is that, though the universe is not in itself a formal system, the "best" way of understanding it involves constructing more and more comprehensive and sophisticated consistent formal systems, each one capturing more aspects of the universe than the previous. This is fairly close to being a rephrasing of Charles S. Peirce's philosophy of science.

It seems nice to refer to these two perspectives as Inconsistent versus Consistentist views of the universe. (Being clear however that the inconsistency and consistency refer to models of the universe rather than the universe itself.)

Potentially the Inconsistentist perspective ties in with a previous thread in this blog regarding the notion of Subjective Reality. It could be that, properly formalized, the two models

A) The universe is fundamentally subjective, and the apparently objective world is constructed out of a mind's experience

B) The universe is fundamentally objective and physical, and the apparently subjective world is constructed out of physical structures and dynamics

could be viewed as two

individually logically consistent

mutually logically inconsistent

separately useful

models of the universe. If so, this would be a concrete argument in favor of the Inconsistentist philosophical perspective.

Inconsistentism also seems to tie in with G. Spencer Brown's notion of modeling the universe using "imaginary logic", in which contradiction is treated as an extra truth value similar in status to true and false. Francisco Varela and Louis Kauffmann extended Brown's approach to include two different imaginary truth values I and J, basically corresponding to the series

I = True, False, True, False,...

J = False, True, False, True,...

which are two "solutions" to the paradox

X = Not(X)

obtained by introducing the notion of time and rewriting the paradox as

X[t+1] = Not (X[t])

In Brownian philosophy, the universe may be viewed in two ways

timeless and inconsistent

time-ful and consistent

Tying this in with the subjective/objective distinction, we obtain the interesting idea that time emerges from the feedback between subjective and objective. That is, one may look at a paradox such as

If this describes the universe then it would follow that the subjective/objective distinction only introduces contradiction if one ignores the existence of time.

Arguing in favor of this kind of iteration, however, is a very deep matter that I don't have time to undertake at the moment!

I have said above that it's better to think of formal systems as modeling the universe rather than as being the universe. On the other hand, taking the "patternist philosophy" I've proposed in my various cognitive science books, we may view the universe as a kind of formal system comprised of a set of propositions about patterns.

A formal system consists of a set of axioms.... OTOH, in my "pattern theory" a process F is a pattern in G if

F produces G

F is simpler than G

So I suppose you could interpret each evaluation "F is a pattern in G"as an axiom stating"F produces G and F is simpler than G"

In this sense, any set of patterns may be considered as a formal system.

I would argue that, for any consistent simplicity-evaluation-measure, the universal pattern set is a consistent formal system; but of course inconsistent simplicity-evaluation-measures will lead to inconsistent formal systems.

Whether it is useful to think about the whole universe as a formal system in this sense, I have no idea...